Besides JEM [1]} that we discussed in the introduction, [2]} is an earlier work that derives a generative CNN model from the commonly used discriminative CNN by treating it as an EBM, where
the authors factorize the loss function \(\log p(\mathbf {x}|y)\)  as an EBM. Following-up works, such as [3]}, [4]}, scale the training of EBMs to high-dimensional data using SGLD. However, all of these previous methods define \(p(\mathbf {x}|y)\)  or \(p(\mathbf {x})\)  as an EBM, while our GMMC defines an EBM on \(p(\mathbf {x},y)\)  by following a mixture of Gaussian distribution, which simplifies the maximum likelihood estimation and achieves improved performances in many discriminative and generative tasks.
